In this topic you will explore the following concepts Features of a quadratic function, plotting points to draw quadratic graphs, Sketching parabolas of different forms of quadratic equations eg. turning point form.
VOCABULARY: axis of symmetry, parabola, dilation(width), reflection, translation(shift), maximum, minimum, turning point, vertex.
Abbreviations eso – every second one CLASSPAD - graphics calculator
Classroom Activities
Consolidation Tasks
Enrichment & Extension Activities
Homework
0
Learning Outcome Students will sort, connect and make sense of information given to solve a mystery question
“Does Amelie make it to the Catwalk” Investigation
“Does Amelie make it to the Catwalk” Investigation
1
Learning Outcome – Key features of the quadratic graph Students will identify what the key features of a parabola are, and by answering specific questions they will show their understanding of each feature
Quiz, Quiz, Trade Activity
Worked Examples
Ex 11A Q1-6
12B Key Features of parabolas worksheet (4 questions)
2
Learning Outcome Plotting points to draw graphs of quadratic functions Students will apply their knowledge of substitution to obtain the co-ordinates of enough points to draw a parabola
Skillsheet 11.2 (Substitution practice)
Pg 457 Ex 11B Q1, Q2ab
Puzzle 10.4
Watch this to get an overview about the parts of a parabola and how to graph them
Just do the first 2 slides - the rest gets a bit hard - good extension
Learning Outcome – Investigation of Quadratic Graphs Student will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph (links lessons 4, 5, 6, 7)
First transformation: What happens when we introduce a coefficient for x2?
Year 9 Mathematics Task Booklet This can be done interspersed with the text work or as a whole to be consolidated with the exercises
Summary Notes
Make your own parabola (y=x2) template to help you sketch them
Graphing grids also available
Pg 460 Ex 11C Q1- 5
P461 Ex 11C Q7-10
30 minutes to catch up on exercises, worksheets and review work
4
Learning Outcome – Investigation continued Students will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph
Second transformation: Parabolas of the form y=ax2 + c What happens when a constant is added to x2
Year 9 Mathematics Task Booklet This can be done interspersed with the text work or as a whole to be consolidated with the exercises
Summary Notes
Pg 464 Ex 11D Q1, 2, 3, 4, 5, Q6adf,7, 8
Every one should look at these these are good animations showing parabolas and how changing the formula moves the parabola
Learning Outcome – Investigation continued Students will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph
Third transformation: Parabolas of the form y=(x – h)2 What happens when a constant is added/subtracted before squaring?
Year 9 Mathematics Task Booklet This can be done interspersed with the text work or as a whole to be consolidated with the exercises
30 minutes to catch up on exercises and review work
6
Learning Outcome – Investigation continued Students will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph
Combining all transformation: Parabolas of the form y=(x – h)2 + c
Year 9 Mathematics Task Booklet This can be done interspersed with the text work or as a whole to be consolidated with the exercises
Summary Notes
P468 Ex 11F Q1, 2, 3 ESO, 4, 5,
P474 Ex 11F Q 6-8
Worksheet: What do you know about the parabola?
7
Learning Outcome – Sketching Parabolas in the Factorised Form Students will determine the x-intercepts, y-intercepts and turning points to sketch parabolas in the form y = (x + m) (x + n)
Sketching Quadratic Graphs (type 1,2 &3) sheets
Worked examples
Pg477 Ex 11G Q1 ace, 2 ESO
P474 Ex 11G Q 3
30 minutes to catch up on exercises and review work
8
Learning Outcome – Applications Students will apply what they learnt to solve practical problems
Worked examples P479 Ex 11H Q 1-5
P479 Ex 11H Q6-8
9
Learning Outcome 3 Different Forms of a Quadratic Equation Students will manipulate the 3 different forms of a quadratic equation
Worksheet: Revision- Different forms of a Quadratic Expression.
Time Rider Task Featuring Laura Craft
Chapter Review and Own Revision
10
TASK CENTRE ACTIVITY [Nine Work-Station Activities]
Features of a quadratic function, plotting points to draw quadratic graphs, Sketching parabolas of different forms of quadratic equations eg. turning point form.
eso – every second one
CLASSPAD - graphics calculator
Students will sort, connect and make sense of information given to solve a mystery question
Investigation
Investigation
Key features of the quadratic graph
Students will identify what the key features of a parabola are, and by answering specific questions they will show their understanding of each feature
Worked Examples
Plotting points to draw graphs of quadratic functions
Students will apply their knowledge of substitution to obtain the co-ordinates of enough points to draw a parabola
Pg 457 Ex 11B Q1, Q2ab
Watch this to get an overview about the parts of a parabola and how to graph them
Just do the first 2 slides - the rest gets a bit hard - good extension
http://www.mrperezonlinemathtutor.com/A2/6_2_Parabola_Formula_Graphing.html
try this animation that shows how to plot a graph
http://www.coolmath.com/algebra/Algebra1/11Quadratics/07_intrographing.htm
Investigation of Quadratic Graphs
Student will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph
(links lessons 4, 5, 6, 7)
First transformation: What happens when we introduce a coefficient for x2?
This can be done interspersed with the text work or as a whole to be consolidated with the exercises
Make your own parabola (y=x2) template to help you sketch them
Graphing grids also available
Pg 460 Ex 11C Q1- 5
Students will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph
Second transformation: Parabolas of the form y=ax2 + c
What happens when a constant is added to x2
This can be done interspersed with the text work or as a whole to be consolidated with the exercises
Pg 464 Ex 11D
Q1, 2, 3, 4, 5, Q6adf,7, 8
Every one should look at these
these are good animations showing parabolas and how changing the formula moves the parabola
http://www.clausentech.com/lchs/dclausen/algebra2/lecture_notes/conics/parabola_animations.htm
Movies of parabolas
note that some of these are a bit advanced but not beyond you
http://jwilson.coe.uga.edu/EMAT6680/Brink/allasgnmts/Graphs3/graphs3.html
PTO
Students will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph
Third transformation: Parabolas of the form y=(x – h)2
What happens when a constant is added/subtracted before squaring?
This can be done interspersed with the text work or as a whole to be consolidated with the exercises
P468 Ex 11E
Q1, 2, 3, 4, 5, 6, 7, 8
watch this again
http://www.clausentech.com/lchs/dclausen/algebra2/lecture_notes/conics/parabola_animations.htm
Students will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph
Combining all transformation: Parabolas of the form y=(x – h)2 + c
This can be done interspersed with the text work or as a whole to be consolidated with the exercises
P468 Ex 11F
Q1, 2, 3 ESO, 4, 5,
Students will determine the x-intercepts, y-intercepts and turning points to sketch parabolas in the form y = (x + m) (x + n)
(type 1,2 &3) sheets
Worked examples
Q1 ace, 2 ESO
Students will apply what they learnt to solve practical problems
P479 Ex 11H Q 1-5
3 Different Forms of a Quadratic Equation
Students will manipulate the 3 different forms of a quadratic equation
[Nine Work-Station Activities]
Practice TEST